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A081141 11th binomial transform of (0,0,1,0,0,0,...). 14
0, 0, 1, 33, 726, 13310, 219615, 3382071, 49603708, 701538156, 9646149645, 129687123005, 1711870023666, 22254310307658, 285596982281611, 3624884775112755, 45569980029988920, 568105751040528536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Starting at 1, the three-fold convolution of A001020 (powers of 11).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (33,-363,1331).

FORMULA

a(n) = 33*a(n-1) - 363*a(n-2) + 1331*a(n-3), a(0) = a(1) = 0, a(2) = 1.

a(n) = 11^(n-2)*binomial(n, 2).

G.f.: x^2/(1 - 11*x)^3.

E.g.f.: (1/2)*exp(11*x)*x^2. - Franck Maminirina Ramaharo, Nov 23 2018

From Amiram Eldar, Jan 06 2022: (Start)

Sum_{n>=2} 1/a(n) = 22 - 220*log(11/10).

Sum_{n>=2} (-1)^n/a(n) = 264*log(12/11) - 22. (End)

MAPLE

seq((11)^(n-2)*binomial(n, 2), n=0..30); # G. C. Greubel, May 13 2021

MATHEMATICA

LinearRecurrence[{33, -363, 1331}, {0, 0, 1}, 30] (* Harvey P. Dale, Dec 15 2014 *)

PROG

(Magma) [11^(n-2)*Binomial(n, 2): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

(PARI) vector(20, n, n--; 11^(n-2)*binomial(n, 2)) \\ G. C. Greubel, Nov 23 2018

(Sage) [11^(n-2)*binomial(n, 2) for n in range(20)] # G. C. Greubel, Nov 23 2018

CROSSREFS

Cf. A001020.

Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), this sequence (q=11), A081142 (q=12), A027476 (q=15).

Sequence in context: A028022 A028020 A025130 * A021021 A164750 A100788

Adjacent sequences: A081138 A081139 A081140 * A081142 A081143 A081144

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 08 2003

STATUS

approved

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Last modified December 4 16:41 EST 2022. Contains 358563 sequences. (Running on oeis4.)